Technical Notes
The simplified methodology for preparing preliminary estimates of MFP is
outlined in the June 2005 Monthly Labor Review article, Preliminary
estimates of multifactor productivity growth located at
http://www.bls.gov/opub/mlr/2005/06/art3full.pdf. This methodology is
applied to both the private nonfarm business and private business sectors
and measures are calculated only for the most recent year. Data for all
previous years are identical to the April 9, 2013 Multifactor Productivity
Trends news release (USDL-13-0626).
Capital Services
Capital services are the services derived from the stock of physical assets
and software. Capital services measures constructed for the preliminary MFP
measures are based on less detail only for the most recent year. The
preliminary measures consist of eight asset types as opposed to the 86
asset types for fixed business equipment and software, structures,
inventories, and land included in estimates for all previous years. The
assets included in the preliminary estimates are computers, software,
communications and other information processing equipment, other fixed
business equipment, structures, inventories, rental residences, and land.
Investments, depreciation, and capital income are estimated for each of
these eight aggregates. Capital services are calculated by a chained
superlative Tornqvist index combining stocks of the eight asset
categories, weighted by capital income shares.
Labor Input
Labor input in private business and private nonfarm business is obtained
by chained superlative Tornqvist aggregation of the hours at work by all
persons, classified by age, education, and gender with weights determined
by each groups share of the total wage bill. The preliminary estimates
of 2012 hours worked for the private nonfarm business and private business
sectors are extrapolated from the hours worked reported in the nonfarm
business and business sectors, respectively, in the February 7, 2013
Productivity and Costs news release (USDL-13-0192).
The labor composition index estimates the effect of shifts in the age,
education, and gender composition of the work force on the efficiency
of hours worked. The preliminary MFP labor composition measure estimates
the number of hours worked by each type of worker based on Current
Population Survey (CPS) data. The estimate of the 2012 labor composition
index assumes relative wages across groups remain constant between 2011
and 2012.
Additional information concerning data sources and methods of measuring
labor composition can be found in Cindy Zoghi, 2007, Measuring Labor
Composition: A Comparison of Alternate Methodologies
http://www.bls.gov/bls/fesacp1121407.pdf and in Changes in the
Composition of Labor for BLS Multifactor Productivity Measures
http://www.bls.gov/mfp/mprlabor.pdf.
Combined Inputs
Labor input and capital services are combined using chained superlative
Tornqvist aggregation, applying weights that represent each component's
share of total costs. The chained superlative Tornqvist index uses
changing weights; the share in each year is averaged with the preceding
year's share. Total costs are defined as the value of output less a
portion of taxes on production and imports. Most taxes on production and
imports, such as excise taxes, are excluded from costs; however,
property and motor vehicle taxes remain in total costs.
Capital Intensity
Capital intensity is the ratio of capital services to hours worked
in the production process. The higher the capital to hours ratio,
the more capital intensive the production process is.
In a production process, profit maximizing/cost-minimizing firms
adjust the factor proportions of capital and labor if the price
of one factor is less than the other factor; there would be a
tendency for the firms to substitute the less expensive factor
for the more expensive one. In the short run, changes in hours
worked are more variable than changes in capital services.
Changes in hours worked in business cycles can result in volatility
of the capital intensity ratio over short periods of time. In the
long run an increase in wages relative to the price of capital
will induce the firm to substitute capital for labor, resulting
in an increase in capital intensity.
Output
Private business sector output is a chain-type, current-weighted
index constructed after excluding from gross domestic product (GDP)
the following outputs: general government, nonprofit institutions,
private households (including owner-occupied housing), and government
enterprises. This release presents data for the private business
and private nonfarm business sectors. The private business sector
accounted for approximately 74 percent of gross domestic product in
2011. Additionally, the private nonfarm business sector excludes
farms from the private business sector, but includes agricultural
services. Multifactor measures exclude government enterprises, while
the BLS quarterly Productivity and Cost series include them. The
output measures are based on the National Income and Product Accounts
(NIPA) data released by the Bureau of Economic Analysis (BEA) on
January 30, 2013 but do not reflect the revised data released by BEA
on February 28, 2013. The preliminary estimates of 2012 output for
the private nonfarm business and private business sectors are
extrapolated from the output reported in the nonfarm business and
business sectors, respectively, in the February 7, 2013 Productivity
and Costs news release (USDL-13-0192).
Multifactor Productivity
Multifactor productivity measures describe the relationship between
output in real terms and the inputs involved in its production.
They do not measure the specific contributions of labor or capital,
or any other factor of production. Rather, multifactor productivity
is designed to measure the joint influences of technological change,
efficiency improvements, returns to scale, reallocation of resources,
and other factors on economic growth, allowing for the effects of
capital and labor.
The multifactor productivity indexes for private business and private
nonfarm business are derived by dividing an output index by an index
of capital services and labor input. The output indexes are computed
as chained superlative indexes (Fisher Ideal indexes) of components
of real output.

Footnotes, Tables 1-4
Source: The Bureau of Labor Statistics (BLS) develops productivity
measures using output and compensation data published by the Bureau of
Economic Analysis (BEA), hours data published by other BLS programs, and
capital data supplied by BEA and U.S. Department of Agriculture. Also see
Technical Notes in this release.
(1) The private business sector covers gross domestic product with the
exception of the output of general government, government enterprises,
non-profit institutions,the rental value of owner-occupied real estate,
and the output of paid employees of private households. The
private nonfarm business sector further excludes farms but includes
agricultural services.
(2) Output per combined units of labor input and capital services.
(3) Gross domestic product originating in the sector, chained superlative
index.
(4) Index of hours at work of all persons including employees, proprietors,
and unpaid family workers, classified by age, education, and gender.
This chained superlative index is computed by combining changes in the
hours of each age, education, and gender group weighted by each groups
share of the total wage bill.
(5) A measure of the flow of capital services used in the sector. Capital
services measure the services derived from the stock of physical assets
and software. The assets included are fixed business equipment, structures,
inventories, and land.
(6) The growth rates of labor input and capital services are combined by
weighting with their respective shares of current dollar costs, and
aggregating into a chained superlative index.